Download Program - Michael Harrison, composer and pianist

Revelation: Music in Pure Intonation
Program Notes by the Composer
Prelude
The “Revelation” tuning presents sonic opportunities that have opened new vistas for me as a
composer and performer. My hope is that I have created a work that is both rewarding to play and
inspiring to hear. In composing Revelation, I wanted to explore the piano’s extensive capacity for
resonance, as well as open the listener’s hearing for an infinite matrix of tones available in just
intonation and the pulsating, shimmering sounds of the commas (see sections on “just intonation”
and “commas” below). My aim is to expand the harmonic, textural and acoustical palette of the
piano as well as enlarge the scope of pianistic techniques. Both the music and tuning for Revelation
were directly inspired by La Monte Young’s magnum opus The Well-Tuned Piano (1964-73-81present). During the 1980’s I worked extensively with Young as his apprentice, tuning and learning
to play his work. I hope that Revelation can also be a springboard for other composers and
performers to continue exploring “just” tunings and return to the ancient roots of music as an artistic
expression of perfect mathematical relationships.
My first major piano work in just intonation was From Ancient Worlds (New Albion Records, 1992),
which was recorded in the reverberant acoustics of the Cathedral of St. John the Divine in New York
City. Revelation represents the evolution of the concept I began with in From Ancient Worlds.
Some of the performance techniques and systems for controlling sympathetic resonance that I use in
both of these works are derived from working with La Monte Young on The Well-Tuned Piano. For
example, Young invented a unique technique for playing extremely fast permutations and
combinations of specific sets of pitches between both hands which he called “clouds.” In
Revelation, I have expanded upon this technique to create four “tone clouds” that form the
cornerstones and ultimate climax of the work.
I am extremely grateful to have had such an extended immersion in Young’s visionary work, which
has opened a way of composing and listening to intervals that has guided me to find my own path
and voice within this new cosmology of sound.
Revelation
In November of 1999, I was one of four American composer/pianists – along with Philip Glass,
Terry Riley, and Charlemagne Palestine – invited to perform at the 4 Pianos festival in Rome. We
performed on four Steinway concert grand pianos, one for each of us, in the center of the high dome
at the Palazzo delle Esposizioni, with the piano lids removed so that the audience could sit in a circle
around us and the music could reverberate throughout the space. Both Terry Riley and I had our
pianos tuned in our own unique and different versions of just intonation. The intensive experience
of rehearsing and performing my own work, as well as hearing the music of my colleagues was
extremely inspiring. As the week progressed, I found myself contemplating the sonic effects that
result from working with “commas” (two slightly different versions of the same note derived at from
different harmonic or mathematical means). I woke up on the morning following the last concert
with a radical new tuning in my mind. It came to me very clearly, seemingly with no planning or
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effort, with all of the mathematical proportions worked out in a well-balanced symmetrical
configuration on the keyboard. It felt like a gift; however, I am aware that this moment could only
have happened as a result of twenty years of working with just intonation tunings.
Upon returning to my music studio in New York City, I applied this new tuning to my customized
“harmonic piano” (see below) and began composing a new work based on the tuning's unusual
qualities. I have titled both this new composition and the tuning “Revelation.” As I experimented
with the Revelation tuning, I discovered that it possessed unique capabilities that I had rarely heard
or encountered before. By combining carefully selected pitch relationships with various
performance techniques, this tuning creates undulating waves of shimmering and pulsating sounds,
with what sound like “phase shifting” and “note bending” effects and other acoustical phenomena.
In some of the tone clouds the overtones are so audible that many listeners have described the
experience of hearing the sounds of many different instruments resonating from the piano. The
tuning has so many beautiful and exotic sounds latent within it, that for the first few months, every
time I played it, I discovered new harmonic regions and felt like an explorer in unknown and distant
realms.
Revelation has twelve interconnected sections in various key centers. Originally, the main thematic
material for most sections of the work was composed but the tone clouds incorporated structured
improvisation using a set of pre-determined pitch relationships and repetitive rhythmic patterns to
develop complex sustained harmonic resonances with unusual acoustical effects. In order to
optimize these effects I wanted to be flexible enough to vary what I was playing in response to what
I was hearing. The exact nature of these effects would vary according to resonances of the
instrument, the precision of the tuning, the acoustics of the performance space, and even variations
in temperature and humidity. However, while working on a score that would enable pianists other
than myself to play the work, I eventually decided to notate the tone clouds, with their complex,
shifting rhythmic patterns. As I scored the work I found that I could more fully develop the themes
and material by writing everything out rather than leaving the development to the discretion of the
performer. However, now that the crystallized, notated version of the work is complete I still enjoy
improvising at the end of each tone cloud in response to all of the unique resonances that develop
with the piano and acoustics of the performance space.
I performed the world premiere of the original version of Revelation in July of 2001 at Germany’s
Klavier Festival Ruhr, followed by the U.S. premiere in October 2001 at Composers Collaborative’s
Solo Flights festival at Lincoln Center. The grammy-nominated pianist Joshua Pierce gave the
world premiere of the new complete version at New York City’s Merkin Concert Hall in February of
2005. Additional revisions were made prior to the Cantaloupe Music recording, which was released
in October 2007. The final score, now about 250 pages in length, is the culmination of my work to
date.
My Work with Just Intonation Tunings Applied to the Piano
My initial fascination with pure tunings stems from my interest in North Indian classical music,
which I began singing and studying in 1978 with one of India’s master vocalists, Pandit Pran Nath
and his earliest American disciples, La Monte Young and Terry Riley. Singing Indian ragas while
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accompanying myself on the tambura, a resonant Indian string instrument, awakened my ears to the
beauty of just intonation. As I became more familiar with the intonation of the Indian ragas, the
compromises of equal temperament, the tuning used on the modern piano, sounded increasingly "out
of tune" and disturbing to my newly sensitive hearing. I began exploring the application of just
intonation to the piano and these two musical worlds came together for me, opening the door to a
new musical universe.
In 1980, seeking the guidance of the most innovative composer working with just intonation, I came
to New York City to study with the minimalist pioneer, La Monte Young. Throughout the ensuing
decade, I worked closely with Young executing all of the specialized tunings and transcribing the
scores for his 6-1/2 hour magnum opus The Well-Tuned Piano. In 1987, I became the only other
person besides Young to perform this work. The previous year I had created the “harmonic piano,”
an extensively modified seven-foot grand piano with the ability to alternate between two different
tunings, thus creating the possibility to play 24 notes per octave on a conventional keyboard. The
unique features of my instrument evolved from Young’s custom designed Bösendorfer Imperial
grand. My harmonic piano allowed me a range of tuning precision and tonal flexibility of
unprecedented scope. (For clarification the term “harmonic piano” refers to my extensively
modified grand piano, while the term “harmonically tuned piano” refers to re-tuning a standard
grand piano to one of my just intonation-based tunings.)
The Matrix of Just Intonation
“Just intonation,” or “pure” tuning, is the universal foundation for harmony which is constructed
from musical intervals of perfect mathematical proportions. Pythagoras and other ancient Greek
philosophers and mathematicians discovered that musical harmonies arise from mathematical
relationships based on whole numbers. The most consonant harmonies are created when two strings
vibrate in simple musical proportions, for example, the two notes comprising an octave have a 2:1
relationship, where the higher note is vibrating exactly twice as fast as the lower note. A perfect
fifth is a 3:2 relationship, a perfect fourth is 4:3, a pure major third is 5:4, a pure minor third is 6:5,
and so on. Revelation uses some of these simple combinations, and much more complex
relationships such as the extremely minute interval of 64:63 (which I call the “celestial comma”),
which forms the nucleus of the work. Young was the first composer to feature the interval 64:63 in
music in such works as Pre-Tortoise Dream Music (1964), The Well-Tuned Piano, and in the Music
and Light Box (1967-68) sculpture, where it is produced by sine waves and sustained continuously as
the only interval in the work. Every different whole number ratio corresponds to a different musical
interval. Because there are an infinite number of whole number ratios there are also infinite matrixes
of tones waiting to be explored.
Just intonation is the basis for the music of ancient Greece, as well as many other cultures, including
those of India, Persia, China, and Japan. Just intonation is also vital to the "a cappella" music of the
West, from Gregorian chant and renaissance polyphony, to "barbershop" harmonies.
Over the centuries the purity of these natural musical proportions was gradually compromised to
facilitate chord changes and modulation between various key relationships. This culminated in a
tuning, called “equal temperament,” that has been the standard for the modern piano for over a
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hundred years. This contemporary tuning divides the octave into 12 equal half steps, like dividing
the face of a clock into twelve hours. The result is a musical democracy in which “all tones are
created equal,” in place of the natural hierarchy based on the fundamental principles of harmony.
During the 17th and 18th centuries equal temperament was not considered musical because it severely
compromised the acoustical purity and beauty of sound. The resulting identical harmonic
relationships of each key were considered almost colorless and bland by comparison with just
intonation and other “non-equal” temperaments such as Mean-Tone and the Werckmeister tunings.
However, by the mid-19th century, increased harmonic complexity stretched the limits of tonality to
the point where equal temperament became a necessity and the universally accepted tuning of the
Western world. In this compromised system every interval except the octave is slightly “out of
tune.” In contrast, harmonies in just intonation ring with clarity and stability, and when certain
complex ratios are used, the music shimmers with exotic resonance.
The Emancipation of the Comma
Revelation continues the innovations first introduced in Young’s The Well-Tuned Piano, with the
extensive use of simultaneously sounding “commas” (two slightly different versions of the same
note derived from different harmonic or mathematical means). These commas exist only outside the
confines of the twelve notes tones of equal temperament. In fact, tempered tunings were developed
over the past four hundred years precisely to avoid the commas that are heard whenever music with
moderately complex harmonies is played in just intonation. I have discovered that incorporating the
commas into the harmonic fabric of my music frees it from the need for tempered tunings and opens
up a new approach to modulation and tonality.
Throughout the history of Western classical music there has been a gradual evolution from the use of
relatively wide and consonant intervals to increasingly narrow and more dissonant sounding
intervals. For example, organum, early two-part music that developed from the 9th to 12th centuries,
used the consonant open sounding intervals of perfect fourths, fifths and octaves. In the 15th and 16th
centuries, the relatively dissonant intervals of seconds, thirds, and sevenths were interwoven into the
polyphonic fabric of the music, which was mainly organized contrapuntally. At the beginning of the
18th century, as music began to be more formally organized around tonal centers with the use of
more modulation, major, minor, and other key relationships developed, and it became essential to
create a tuning system that permitted moving easily between different key centers. In the 19 th
century, the evolution of even more complex chromaticism resulted in stretching tonal harmony to
its limits. In the 20th century, Schoenberg’s concept of “emancipation of dissonance” led to the free
use of any interval combination in equal temperament. I propose that this evolution is still in
progress, and that its next stage is the “emancipation of the comma.”
Perhaps the most famous comma, and the easiest to understand, is the Pythagorean comma
(originally discovered by Pythagoras). This is the slight difference that exists between any note and
the almost identical note that results after tuning around a “spiral” of 12 perfectly tuned fifths from
that first note. For example if you start with the note C and tune a series of 12 perfect fifths as
follows: C - G - D - A - E – B - F# - C# - G# - D# - A# - E# - B#, the resulting B# will be slightly
higher in pitch than the original note C that you started tuning from, if it is tuned in the same octave.
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The minute difference between the tuning of this note B# and the original C is the Pythagorean
comma (approximately 1/8 of a semi-tone). In equal temperament these fifths are each tuned 1/12 of
a Pythagorean comma flat so that the B# and C are equalized to become the same pitch. As a result,
the naturally occurring “spiral” of “perfect” fifths is squeezed into a “circle” of “imperfect” fifths.
In addition to the Pythagorean comma, there are many other commas that result from other slight
mathematical differences in the calculation of tones. In the development of Western music, efforts
were made by composers and theorists to emphasize consonance and to minimize and regulate
dissonance. Certain intervals were allowed in different contexts, and others were entirely avoided.
Some combinations were deemed to be “good” and others “bad.” For example, the augmented
fourth, or tri-tone, which was the so-called “devil in music,” as well as any “wolf” tones (the
concurrent sound of any two notes whose corresponding fifths or octaves sound a comma apart),
were rigorously avoided. Numerous different “unequal” tempered tuning systems, such as MeanTone and the Werckmeister and Kirnberger tunings, were developed both to distribute the comma
around a predetermined octave and to minimize the effect of these “wolf” tones. As a result, music
could be played in a larger array of tonal centers without the “disagreeable” effect of the commas
being heard. This was necessary for keyboard and fretted instruments, however, it was not a
problem with the voice or string instruments that were able to play subtly different versions of the
same pitch so as to avoid the commas. In equal temperament all commas are completely obliterated
by their equal distribution among all 12 keys so that they are no longer audible. As a result,
however, every interval except the octave is distorted in its purity of tuning: perfect fifths are
narrow, perfect fourths are wide, and major thirds are 14% of a semi-tone sharp, etc.
As the development of my music and tunings has unfolded, I have become increasingly interested in
the special sonorities and acoustical effects created by juxtaposing and combining various commas.
In 1980, I was exploring different just intonation tunings where I had tuned D and D#, and A and A#
to slightly different versions of the same note (i.e., a syntonic comma, also called the diaschisma, or
81:80 ratio, apart). In one of my practice sessions I found that if these adjacent notes were played in
rapid succession an immediate periodic pulsating pattern was generated by the pitches themselves.
Using a technique that was first discovered and demonstrated by La Monte Young in his concerts
and recordings of The Well-Tuned Piano, I synchronized the rhythm of my playing with the
rhythmic pulsations of the acoustical beats generated by the pitches themselves in order to achieve
an organic link between pitch and rhythm. I was so captivated by the resulting sounds that I played
fast “cloud-like” patterns without interruption for about 8 hours.
In my previous major work for piano in just intonation, From Ancient Worlds, simultaneously
sounding commas occur in the overtones of certain sections, creating shimmering and pulsating
effects. Revelation takes this concept to another level by incorporating three sets of adjacently tuned
“septimal” commas (the 64:63 ratio, or approximately an “eighth” tone) into the harmonic fabric of
the tuning. When they sound simultaneously or in rapid succession, they produce rarely heard
combinations of modes, harmonies, and acoustical phenomena. The comma is thus freed from its
restricted status as an "out-of-tune" dissonance that, until recently, was disguised, avoided or
obliterated by tempered tunings, compositional styles, performance practices and instrument designs.
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The “Revelation” Tuning
The Revelation tuning divides the octave into twelve “unequally” spaced notes, all of which are
tuned to overtones of a fundamental low F. These twelve select overtones are subsequently
duplicated throughout the range of the piano by octaves. The tuning is extremely unusual in that it
does not even have a chromatically ascending scale. These pure intervals are tuned by ear, based on
the acoustical beats in their resonances.
The tuning's unique qualities exist in the relationships between the black and white keys, which
reveal a wide variety of exotic and colorful intervals. The Revelation tuning has a practical
symmetry whereby all of the white keys form a series of Pythagorean fifths (a 3:2 ratio), and all of
the black keys form another series of Pythagorean fifths, with each black key tuned to the seventh
overtone (a 7:4 ratio) above each corresponding white key. The 7:4 ratio is the naturally occurring
minor seventh that exists in the overtone series (approximately 31% of a semi-tone flat from the
equal tempered minor seventh). As a result, three black keys in every octave are tuned to the
“celestial” comma (the 64:63 ratio, also referred to as the “septimal” comma) below three adjacent
white keys. This creates ample opportunity to use what I refer to as the “pulsating comma effect” in
a variety of different harmonic contexts, where the adjacent commas sound simultaneously. This
symmetrical layout of the white and black keys also allows for a very intuitive approach to playing
the piano. For example, the white keys are purely diatonic; by adding any black keys into the mix
you will get either “septimal” minor intervals or the “pulsating comma effect.”
The twelve pitches are tuned to the following twelve partials (or “overtones”) of the fundamental
note F. For white keys: F=1, C=3, G=9, D=27, A=81, E=243, and B=729 (all of which are multiples
of the prime number 3); and for black keys: E-flat=7, B-flat=21, F#=63, C#=189, and G#=567 (all of
which are multiples of the primes 3 and 7). The concept of creating a tuning based entirely out of
the primes 2, 3 and 7 is something that I learned from La Monte Young who first introduced the idea
in The Well-Tuned Piano. In this way the Revelation tuning uses the same set of “ingredients” as the
Young’s tuning for The Well-Tuned Piano, however the exact “recipe,” or configuration of the tones
on the keyboard, is quite different.
Postlude
Creating this work has been an incredible journey, and, as a composer and performer, I am
exhilarated by the sonic possibilities this has afforded me. When I listen to Revelation, either on the
recording or as a member of the audience, I am amazed by the piano’s natural beauty, range of color,
and the power that it is capable of evoking. The piano is one of the most resonant instruments in the
world, but the equal tempered tuning system now in use impedes this natural resonance in favor of a
convenient, democratization of the twelve tones and key relationships. Just intonation tuning frees
the piano from these restraints, further revealing and maximizing its natural resonances. When the
commas are allowed to sing out, they create a new and beautiful complex acoustic universe.
© 2007 Michael Harrison, New York City
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